A toy analyst at market research firm Mintel said Lego’s recovery had been fuelled by its investment in quality and design. Photograph: Graeme Robertson

It is a brand name familiar to children around the world, but a decade ago Lego was in crisis. Sales were collapsing at a rate of 26% a year, it lost 1.4bn Danish kroner (£150m) in 2003 and private equity firms were circling the 82-year-old family-owned Danish company.

Now, after a series of job cuts and the ending of the family's management of the company, the plastic brick business has rebuilt itself into the world's most profitable toy maker ahead of Barbie's Mattel.

The company, which has been headquartered in the small Danish town of Billund (population 6,155) since 1932, has reported "another record breaking year" of sales and profits growth – for the ninth consecutive year. Its high profitability comes from its ability to turn each kilogram of raw material plastic – which costs less than $1 – into sets that sell for more than $75 per kg.

Annual profits increased by almost 10% to 8.2bn kroner (£900m) – about the same as the profit Facebook turned in last year. Sales jumped 10% to 25.3bn kroner (£2.8bn).

"That is an incredible quadrupling of our revenues in less than 10 years," Joergen Vig Knudstorp, Lego chief executive, said. "We think we are changing children's lives forever when they play with Lego. We think this was another year where we got great affirmation of that."

Knudstorp is credited with driving Lego's resurgence since he took over as CEO from Kjeld Kirk Kristiansen, grandson of the company's carpenter founder, during the 2003-4 crisis.

He said Lego's success was due to constant innovation and the creation of 60-70 new products every year, including Harry Potter, Star Wars and SpongeBob SquarePants ranges. But he admitted it is still a "major innovation challenge" to "stay on the top of children's wish lists" against competition from iPads and computer games. "We need to constantly become better, or otherwise there will be someone out there who will catch up to us," he said.

Jane Westgarth, a toy analyst at market research firm Mintel, said Lego's recovery had been fuelled by its investment in quality and design. "They are doing things that are taking Lego into a slightly different position, from the boxes of bricks where you had to use your imagination to sets you use in specific ways with characters you already know," she said. "If it's good quality, people are prepared to pay that little bit extra."

Westgarth said Lego was also benefiting considerably from parents' nostalgia for their own childhood – parents including David Beckham, who admitted earlier this month that he builds Lego with his children to stay calm and had just completed the 4,287-piece Tower Bridge kit. "For a parent aged 30 there's no doubt about it that they would have Lego in their homes. Parents like to introduce their children to things that they loved as children."

The company, which sold its Legoland theme parks to Madame Tussauds owner Merlin Entertainments in 2005, is building on its "red core business" by boosting its digital presence, but Knudstorp said his customers have done most of the work for him.

More than 99% of Lego videos on Youtube – featuring Lego recreations of everything from the London 2012 Olympics to the New Testament – are made by users. "We're not leaving the brick, but we will leverage digital technology to stay relevant over the next 20 years," he said.

Lego, which is derived from the Danish "leg godt" meaning "play well", is also benefiting from "a considerable amount of excitement" prompted by the Lego Movie. The film, which features the hit Tegan and Sara song Everything is Awesome, is taking £2m a day in UK cinema box offices, and has topped the US and Canadian charts for three consecutive weekends.

Next up is Knudstorp's "pretty simple ambition" to "take the bricks all over the world". Lego is sold in more than 130 countries round the world, but Knudstorp admits that "we're not really there" in many of the world's less well off nations.

"We see a huge opportunity to bring Lego further out into the world in the next 20 years," he said.

Sales in China, where Lego will open a new $300m factory in 2016, grew by more than 50% last year - although from asmall base. Knudstorp believes Lego could be expanded to 600m Chinese customers within in the next decade."But we need a set up that is much more diverse, much more international, than we are today.

"It would be arrogant to think that just because you're Danish you're equally knowledgeable about what it takes to succeed in countries all over the world," he said. "We want to remain very much a Danish company rooted here in Billund, a place where we were born and we have our heritage and we will never leave.

"But we want to be a Danish company that's welcoming to all sorts of cultures."

To do so the company is diversifying senior management into four global offices in London, Singapore, Shanghai and Connecticut.

The company is still owned by the descendents of Ole Kirk Kristiansen, a master carpenter and joiner who founded the company in Billund in 1932, when it was a small village. Ole's son Godtfred joined the firm when he was 12 years old, and the company's first toy was a wooden duck called Lego. The first plastic bricks were produced in 1949.

Godtfred's son Kjeld Kirk Kristiansen was chief executive from 1979-2004. Forbes magazine named Kjeld as Denmark's richest man with a net worth of $7.3bn in March 2013. A spokeswoman declined to comment on the family's current wealth.